x+3y=18 and -x+2y=7

Question

solving systems of equations by graphing or using a table

Answer 1

x + 3y = 18, -x + 2y=7 first thing you do is get it into the y = mx + b format, you do this by solving for y.

x+3y=18 first subtract x from both sides

3y=18-x now divide both sides by 3

y= (18-x)/3 or  y= 18/3  - x/3

y= 6 - x/3 now rewrite it as x/3 is the same as 1/3x

y=-1/3x + 6

 

Now for the other one, -x + 2y = 7  add x to both sides

2y= 7+x  now divide each side by 2

y = 7/2 + x/2  or   y= 1/2x + 7/2

now make a T table with one side being x, and the other being y, on the x, put -2,-1,0,1 then calculate the y values for the x values for both equations

for the first equation: y = -1/3x+6

x:                    y

-2                  6.6667

-1                  6.3333

0                    6

1                   5.6667   now plot these points, make more points if you need to

for the second equation: y=1/2x+7/2

x:                                  y:

-2                             2.5

-1                               3

0                                3.5

1                                4    now plot these

 

Happy new years

Answer 2

Since these are a system of equations you can also use the elimination method.

x + 3y = 18

-x+ 2y= 7 now draw a line and add the 2 equations, the x cancel out

5y = 25  divide each side by 5

y=5   now plug this in to get the x value into either equation

x + 3(5)=18

x+15=18

x=3  y=5

 

if you do it the first way, if you graph both lines they will intersect there. This is elimination method but since your teacher wants graphing/table method the first way is what she is looking for.

Happy new years.